Rigidity Theorems for Diameter Estimates of Compact Manifold with Boundary
Let (N,g) be an n-dimensional complete Riemannian manifold with nonempty boundary ∂N. Assume that the Ricci curvature of (N,g) has a negative lower bound Ric≥−(n−1)c2 for some c>0, and the mean curvature of the boundary ∂N satisfies H≥(n−1)c0>(n−1)c for some c0>c>0. Then a known result (cf. ) says that supx∈Nd(x,∂N)≤1ccoth−1c0c. In this paper, we prove the rigidity result that if N is compact, then the equality holds if and only if (N,g) is isometric to the geodesic ball of radius...[Show more]
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|Source:||International Mathematics Research Notices|
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